Nicki Minaj is having her photo taken. I've never seen anything quite like it – so incisive, dramatic and bossy. "No close-ups," the rapping pop star growls. Then she kittens up to the camera, pouts, thrusts, threatens, giggles and pleads. Each pose lasts a split second. Blink and you miss it. Miss it, tough luck. The photographer looks shell-shocked. He's got more, and less, than he bargained for. "I think that's enough, thank you," she says. She walks over to him, wiggling her astonishing cartoon bottom like a rudder. "Let me see what it looks like," she says. "OK, that's enough."

For years, Minaj rapped for the stars – she had bit parts on hits by Ludacris, Lil Wayne, who mentored her, and perhaps most famously Kanye West, for whom she contributed a brilliantly grotesque solo on Monster. In 2010, she featured on seven singles in the US charts – a record. Now she's on the verge of being ridiculously famous in her own right – and in the most unlikely manner. Minaj has just released her second solo album, and it has topped the US and UK charts. She has 11 million Twitter fans. Or rather, she did have before she decided on the spur of the moment to quit Twitter last week because a fan had leaked her songs. Typical Minaj. She says she might return, and presumes her fans will wait for her – she might be back by the time you're reading this.

Astonishingly, Minaj, best known for down and dirty raps that outfilth the boys, has found a new niche audience – little girls who still play with Barbies and wear long pink dresses in homage to her. She even calls her girl fans Barbs. She is now probably best known for a performance of Super Bass on the Ellen show, which she gave with eight-year-old fan Sophia Grace Brownlee, backed by her five-year-old cousin Rosie – it's been viewed on YouTube more than 38m times. In the song, a tribute to "a hell of a guy" who sells coke, and a warning to the ladies who might have their eye on him, Minaj raps: "When he give me that look/Then the panties comin' off, unh." On the Ellen show, the girls sing a cleaned-up version, but it is still disarming: a collision of two very different worlds.

Nicki Minaj on the Ellen show with two young fans. Photograph: NBC

Minaj, 29, was born in Trinidad and brought up by her grandmother while her parents made a new life for themselves in America. At the age of five she joined them in Queens, New York. She says she read her way through much of her childhood. "It was an escape." From what? "Bbbbrrrrrrrrrr," she says, with an impeccable impersonation of a ringing phone. "I don't know. In all the books I read, there were big houses and they had all this nice stuff and I always wished that could be my family."

She says her father was an alcoholic and drug addict. Sometimes, she has claimed, she would return home to find furniture missing – flogged to fuel his addictions. Her mother worked as a nursing assistant and did her best to keep Nicki and her younger brother safe. One night she dreamed her husband had burned down the house, and the next day told the children to sleep at a friend's house. That night, she says her father did try to burn down the house – Minaj's mother, the only one at home, managed to escape. Her father has said that her claims are exaggerated.

Her father sounds like a nightmare, I say. "He could be. Especially when he was drinking. It's weird, because when he was on crack, he was more peaceful, and when he would drink, he became loud and violent. Each drug has its own spirit. You could see it on the person and feel it in the room." Was she scared of him? "Of course. I was very, very afraid that he would snap. I wasn't afraid for myself but for my mother. He didn't do anything to me or my brother that made us feel we had to fear him.

"We moved so many times when I was a kid. We were always running away from him. Whenever we got to a new house, he would find us."

How old was she when her parents separated? She looks at me, surprised. "He's still with my mother. He went to rehab and cleaned himself up. Eventually they started going to church a lot, and he got saved and started changing his life. He's away from drugs now. He doesn't instil fear in people any more."

Did that shape her attitude to drink and drugs and men? "Yeah. Definitely to men. I vowed that I'd never allow any man to control me or to be an alcoholic or anything like that around me, because I don't want my children seeing that."

There is no hint of Trinidad in Minaj's voice. It is pure Scorsese Nooo Yoik. She talks quietly, reflectively, which makes the wig and leopardprint shorts and stockings seem a little incongruous. Underneath the pneumatic bosom and bottom (rumoured to be surgically enhanced, which she denies), the gold bangles, the screaming pink and green make-up, there's a rather delicate beauty – lovely big features in a small face. She refuses to talk about her body these days and looks aghast if it's suggested anything might have been worked on.

"Your teeth are beautiful," I say.

"Thank you," she says.

"Are they natural?"

She gives me a ferocious stare "Are your teeth natural?" she replies.

"You can tell they are," I say. "They're disgusting."

Now one of half a dozen big men sitting in the room with us stares at me. "I can see your plaque from here," he says, in an intimidating voice.

Nicki Minaj was born Onika Tanya Maraj, and friends called her Nicki or Cooky. Onika is a nice name, I say. "Thank you." Does she like it? "No, I don't. My rule is, whatever you were calling me four years ago is what you should be calling me now, because I don't like it when my family or close friends call me Nicki Minaj. To me I'm not Nicki Minaj when I'm with them."

Why did Maraj turn into Minaj? "Somebody changed my name. One of the first production deals I signed, the guy wanted my name to be Minaj and I fought him tooth and nail. But he convinced me. I've always hated it." You sense it's the last fight she lost.

But, as she says, Minaj is a character – the ego-maniacal rapper you mess with at your peril. "I feel it's like one big theatre piece. It's a show."

Onika Maraj would make a great Russian doll: inside you get Nicki, and inside her you get any number of minor characters. Her new album is called Pink Friday: Roman Reloaded, a reference to one of her favourite alter egos, Roman Zolanski, an irate gay man. Then there's Martha, Roman's mother, who speaks in a ridiculous Dick Van Dyke English accent on Minaj's collaboration with Eminem, Roman's Revenge. There's also the Harajuku Barbie, who's all high-pitched sweetness and free-spirited fun, Spanish Rosa (pronounced Rrrrrosa), saintly healer Nicki Teresa and Nicki Lewinsky – an alter ego she's dropped since gaining so many young fans.

From where did all these characters come? "My head." How would she describe her head? "Crazy, always going, never stops." Is she a fan of Roman Polanski? She giggles, and says she had heard of him, liked the name, but no, she hadn't seen his films. "I knew how he looked and I thought he was a weird-looking man, confused little soul. I went on Twitter and said, 'From now on my name's Roman', and my blogs went crazy. My Barbs went crazy. They cried and said, Nicki don't change your name, we don't want to call you Roman."

Nicki Minaj with Kanye West. Photograph: Getty Images /Getty Images

She began singing, rapping and inventing characters in her bedroom – again, escape. At six, she told her family she was going to become famous as a soap actress. She studied drama at LaGuardia High School (aka, the Fame School). Kanye West recently called her "the scariest artist in the game" and said that she had the potential to be "the number two rapper of all time" (nobody would beat Eminem, he added). Her acting ability and imagination are integral to her rapping – the characters, accents, flow, enunciation and ability to glue together the most unlikely words. "Saviour of rap for women? I'm a comic book heroine, but when the wind blows in I'm so Marilyn," she raps, in a rare moment of public doubt on the track, Can Anybody Hear Me? She's more likely, though, to be telling fellow female rappers it's not even worth trying to compete with her – "Bitches ain't serious/Man these bitches delirious/ All these bitches inferiors," she raps in Come On A Cone.

Was she always determined to out-brag and out-curse the boys? "Yes, definitely. That's why I say stuff like, 'Dick in your face', because I don't even wanna refer to female genitalia any more." Why not? "I just feel I have bigger balls than the boys."

Has she always felt like that?

"Yes."

"Is that the persona or you?" I ask.

"No, that's definitely me."

"Is that because you don't think boys have big balls, or because you have huge ones?"

Minaj refers so often to her male genitalia, it's not surprising there's been talk about her sexuality. When asked if she thought there could be a successful gay rapper in a notoriously homophobic world, she suggested she was gay. "TMZ were just yelling stuff out to me, and they were like, 'Do you think there'll ever be a gay rapper?' and I said, 'You have one.' It was just in fun." So she likes boys? Silence. Girls? Silence. Both? Silence. Neither? She grins. "Yeah, none." Oh come on! "I don't like any of them. Sexually or otherwise." Minaj says exactly what she wants to: not a word more or less. There are, of course, contradictions aplenty. Her music certainly does not suggest an aversion to sex or sexuality. Nor does her appearance. After rowing publicly with fellow rapper Lil' Kim, who claimed Minaj had borrowed heavily from her, she asked, "Why in the black community have we got to hate on each other? Gaga didn't on Madonna… we're helping each other." Fine sentiments, but in the song Itty Bitty Piggy, she states, "It's like I've just single-handedly annihilated, you know/Every rap bitch in the building". Hardly collegiate.

Actually, she says, on her first album Pink Friday she was determined not to be dirty or boastful. "I wanted to prove the point that I didn't have to rap about it. But I feel like now, my fans speak like that, and I don't have to walk round being a goddamned prude. And my music doesn't need to sound like a prude unless I'm doing a pop song." She says the word "pop" breathily, ironically.

The irony, though, is that filth-spitting Minaj is now better known for pop records for little princesses. Has it surprised her how young her fans are? "Yes, of course. I never thought I'd have young fans. Never." Some older fans are suggesting she's sold out by singing pop. But it's funny, I say, listening to the first mix tapes she recorded…

She finishes off the sentence for me. "…You hear me singing. And that's the thing. I really want you to write that. Because it's the most bullshit thing I've ever heard – you liked me only when I was doing rap. I never only did rap. My first single was called Your Love, and it was a pop song. I did a song called Knockout with Lil Wayne about three years ago. Nobody said anything about that. Why? Because it didn't become huge like Starships. That's what irritates me. People always want to talk about who I was, but I've always been singing, always been experimenting with pop music. So the fact that it got huge one day, should I apologise for that? Should I apologise that Starships and Super Bass did well, and children like them, and Middle America can sing along? There's nothing wrong with that. I'm just broadening my fan base. I think everyone should enjoy music." If she wants to duet on a power ballad with Rihanna, that's her choice, she says.

Doesn't she find it strange, hearing eight-year-old girls, such as Sophia, singing her songs about hos and bitches? "No, she doesn't say ho. She never cursed." Would it worry her if she did? "Of course. I'd be very upset. I don't want children cursing. I'm very strict on my nieces and my little brother. They have to listen to clean versions of music. Even my music."

So she's quite puritanical? "Well, if that's what you call it. But if you asked any adult, 'Would you like your children knowing every part of your life and speaking exactly the way you speak when you talk to adults?', they'd say no, so I'm a firm believer in children remaining children."

Is there pressure to change her image for the children? "Sometimes it feels like I have to change, but I can't. What rapper changes themselves for children?"

"So if some business guru came up to you and said, 'Hey, Nicki, if you lose the swear words…'"

Before the question is out she blows up. "Why do people ask me to lose swear words? Do people ask Eminem to lose swear words? Do they ask Lil Wayne to lose swear words? I did an interview the other day and when I saw it back I'm like, why the hell did she make the interview all about some goddamned kids? It was crazy. Five-year-old children shouldn't be the subject of a Nicki Minaj interview."

Excuse me, I say, trying to interrupt, can I just ask my question: what would you say to the business guru? "Well, first I want you to answer my question, then I'll answer yours."

I'm tempted to say that Eminem and Lil Wayne don't have such impressionable fans, but I don't think that's actually true. "Because it's a sexist world out there and we apply different values to women?" I offer.

"So make sure you put that in your article. Cos we're getting this on tape."

I ask if she wants to write up the interview herself. "No, I just want you to put that in. Don't you think it's strange, though? I used to see Eminem in concert and people were bringing their little brother or whatever. Nobody stops them and says [she adopts a posh English accent], 'Would you stop swearing, Eminem, for loads of money?' I don't get it, I don't get it."

And now there's no stopping Minaj. "On the one hand you have people saying, 'We want her to be hard and raunchy and explicit', and on the other hand there's, 'Nicki Minaj, would you stop swearing for the children, please?' It's like, what d'you want me to be? How many different people can I fucking be?" She's flowing so fast, she's almost rapping.

She stops, once again calm and considered, to say how much she loves her young fans and how she sees herself as a role model. "I tell my Barbs, 'Stay in school, respect your body, don't go giving it away, don't depend on a man.' I tell them that all the time." Who's been her role model? "My mother," she answers instantly. And her heroes? "God. And my mother." Does she consider herself political? "No." Is she going to vote Republican? "Of course not!" she says outraged.

So she is political? She cackles.

On Pink Friday: Roman Reloaded, four of the songs are produced by RedOne, best known for working with Lady Gaga. The cover image confused me, I say. At first glance I thought it was Gaga, or at least a spoof of her.

Minaj gives me a look that could kill at a thousand paces. "You think that looks like Gaga? Absolutely not. I have no idea what you're talking about… Maybe little black kids shouldn't wear blond hair?"

At which point there is much muttering about my manners from the men in the room, and I'm told there is no time for any more questions. But Minaj is more forgiving than her heavies. I tell her that the reason I'd asked about the imaginary business guru was because she appears to take the business side of things seriously. Her face lights up – this time with pleasure. "Absolutely. Everything I do, I do with business in my head. If you're not savvy, this business will eat you alive. A lot of people see it as a big party. And when that party is up, what are you going to do?

"I want to show little girls that the possibilities are endless. That's my goal – to not only do it for myself, but to show them I can do whatever I put my mind to. I don't give a damn if I was born poor, I can come out of this shit with something to offer my children and grandchildren."